A device for preventing an overrunning operation of an internal combustion engine is well known which comprises an ignition failing thyristor so arranged that it is shunted across an ignition thyristor of a capacitor discharge breakerless ignition system, U.S. Pat. No. 3,703,889 discloses such a device for preventing an overrunning operation of the engine. The conventional device bears some problems which need to be solved. One of them is that a voltage produced by a revolution number detecting generator in association with the engine is not always proportional to the revolution number of the engine. In case the generator is operatively associated with a magneto of the engine, which includes a loading coil such as a lamp energizing coil and a battery charging coil as well as an ignition power coil, a voltage established across the revolution number detecting coil varies depending on whether loads act or not, because of an armature reaction of the magnetic circuit in the magneto. Furthermore, the voltage across the revolution number detecting coil also varies on demagnetization of the magnets in the magneto. Another problem is that the ignition failing thyristor has a triggering gate current varying due to its own temperature. That is, as the temperature of the thyristor decreases, larger triggering gate current must be supplied to the gate of the thyristor to trigger it. This causes the occurrence of a hysteresis on repetition of failure and success to ignite the engine. More particularly, when the revolution number per minute of the engine exceeds a predetermined value, the ignition failing thyristor permits the ignition system to be overridden. A current flowing through the ignition failing thyristor causes the pellet in the thyristor to be heated so that smaller triggering gate current triggers the ignition failing thyristor. Therefore, unless the revolution number per minute of the engine is lowered far below the predetermined value, the ignition failing thyristor cannot be turned off. As a result, the revolution number of the engine at which the ignition is resumed is different from that when it begins failure to be ignited by means of the device, resulting in a hysteresis between failure and success to ignite the engine. FIG. 1 shows a hysteresis loop produced between the conditions of failure and success to ignite the engine. Since failure to ignite the engine causes a non-combusted fuel-air compound gas to be exhausted into an exhaust pipe and a muffler of the engine, the hysteresis possibly results in more compound gas accumulated in the exhauster components. As a result, explosion may occur when the engine is reignited. Unpleasant noises may be also produced therefrom. There is an allowable width of the hysteresis loop which is adapted to control the explosion of the compound gas and to restrain unpleasant noises. A thermally responsive element which is arranged adjacent to the anode of the thyristor to detect its temperature cannot improve the hysteresis because it has a low response. Still another problem is that the components of the device is adversely affected by heat from the engine as well as that from the ignition failing thyristor. In this case, it bears no relationship to the hysteresis on the conditions of failure and success to ignite the engine, but the revolution number of the engine at which the device is operated varies as shown in FIG. 2. The curve a of FIG. 2 shows that as the atmosphere temperature decreases the revolution number of the engine at which the ignition failing device is operated tends to increase. In case the engine may be available for a snow mobile, it will be understood that a problem occurs just after it starts.